Show all steps clearly. All quantities must be labeled with mathematical symbols. Do not estimate with your calculator until the very end. train. A train is traveling 0.6 km/min along a straight track, moving in the direction as shown in the figure below. A movie camera, 0.5 km away from the track, is focused on the r: km = km (a) How fast is the distance.from.the.camera to the train changing when the train is 1 km from the camera? Round your answer to 3 decimal places. --Units-- (b) How fast is the camera rotating at the moment when the train is 1 km from the camera? Round your answer to 3 decimal places. --Units--. For instructor's notes only. Do not write in the box below. This answer has not been graded yet 0.5 -Unit (a) How fast is the distance from the camera to the train changing when the train is 1 km from -Units (b) How fast is theam per min Imin the moment when the train is 1 kim from the camera? Ro square km per min For instructor's notes only. Do not write in the box below. This answer has not been graded yet. Submit Answer (a) How fast is the distance from the camera to the train changing when ---Units-.. (b) How fast is the camera rotating, at the moment when the train is 1 kn ---Units--- ---Units-- For instructor's no radians per min write in the box below. radians degrees per min NI - degrees km per min This answer has huruoon grauou youShow all steps clearly, All quantities must be labeled with mathematical symbols. (a) Consider a circular oil slick that forms on the surface of a large lake. When the radius of the oil slick is 160 meters, the radius is expanding by 0.9 meter/minute, At that moment, how fast is the area of the slick expanding? Convert your answer to square meters per second. Give an exact answer me/sec (b) Now let's consider the volume of another circular oil slick. For simplicity, think of the slick as a thin cylinder with uniform height. When the radius of this oil slick is 30 cm and the height is 3 cm, the radius is expanding by R cm/min and the height is decreasing by H cm/min. How fast is the volume of the oil changing in cm /min? Your answer will have R and H in it. cm /min in DZL. You must show all steps clearly and use Use L'Hopital's Rule to evaluate the following limits. Give exact answers. Note - you will need to rewrite the functions first. (a) lim 12yin(y) = For instructor's notes only. Do not write in the box below. This answer has not been graded yet. (b) lim - 1-t- For instructor's notes only. Do not write in the box below. This armever has not been graded yet in this problem you will enter only your final answer here. To receive credit, you will upload your work in the Assignment 6.2 folder in D2L. Show all Find the exact positive value of c if the average values of the function v(x) = on the interval [1, c] is equal to 3. C = For instructor's notes only. Do not write in the box below. 1. [-/4 Points] DETAILS UPLOAD PROBLEM In this problem you will enter only your final answer here. To receive credit for the work, you will upload your work as a PDF in the Assignment tab in DZL. You must show all steps clearly and use proper limit notation throughout. Work must be neatly written. (a) Describe the form of the limit lim "x46+ (1 + x)6/. O 100 (b) Use natural logarithms to evaluate the limit. Give an exact answer. lim. (1 + x)* = V ar's notes only, Do not write in the box below